Answer:
Step-by-step explanation:
We can look at the ratios of differences between x and y values to determine the nature of the sequence.
x-differences
9 -8 = 1; 11 -9 = 2;
y-differences
12 -10 = 2; 16 -12 = 4;
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The ratios Δy/Δx are 2/1 = 2 and 4/2 = 2. That is, the points lie on a straight line with slope Δy/Δx = 2.
The y-intercept of the line can be found using the formula ...
b = y -mx
b = 10 -2(8) = -6 . . . . for (x, y) = (8, 10)
So, the rule relating x and y is ...
y = 2x -6
The value of n is ...
n = 2(14) -6 = 22
